"The Order of the Forces"
ISBN 0-9677172-0-5
 
is a study in nuclear and fundamental particle physics through the Geatron Nuclear Model.
By
Eugene B. Pamfiloff

Notice: This Book Has SOLD OUT.

By
Eugene B. Pamfiloff

Session D34 - Bose-Einstein Condensation and Atomic Molecular and Optical Physics.
ORAL session, Monday afternoon, March 03
Room 2, Austin Convention Center

[D34.001] Gross-Pitaevskii Approximation for the Bose-Einstein Condensation: Green Function Formalism.

Using the Green function method we solved the time-independent, T=O K, one-dimension, Gross-Pitaevskii equation (G-PE) for the Bose-Einstein condensation in dilute atomic alkali gases. We are able to formally obtain an analytical solution for the order parameter \Psi (x) and for the chemical potential \mu as a function of the trapping frequency ømega and the effective interaction constant øverline\Lambda . A Bonn-Neuman iterative procedure is implemented for solving the non-linear system of equations obtained from the G-PE equations into the formalism. Also, we compare the G.f. formalism and two other method of solution: variational (soliton solution) and perturbation theory for the universal parameter, øverline\Lambda /(l\hbar ømega ) (l is the magnetic length), which characterize the atomic gas condensation. Generalization of the above mentioned methods for two order parameter \Psi _i(x); i=1,2 (i.e. two species of alkali atoms) is also presented.

[D34.002] Soliton solution of Gross-Pitaeviskii equation with harmonic trap and gravity potential

The inverse-spectral-transform method of solution is shown to be applicable to dynamics of Bose-Einstein condensation of Gross-Pitaeviskii equation with the harmonic trap potential and gravity potential, i¦×_t +¦×_xx +2|¦×|^2 -V(x)¦×=0. The method determines the class of solutions that are symmetric or antisymmetric in x. This is done with the help of a modification of the Ablowitz-Kaup-Newell-Segur and Zakharov-Shabat formalism incorporating an x- and t-dependent eigenvalue par ameter ¦Æ, together with a transformation of variables. Finally, we comment on the extension of the analysis to explicitly time-dependent potentials or inhomogeneities V(x,t). We examine the one-soliton soution of Gross-Pitaeviskii equation with the harmonic trap potential and gravity potential, i.e., V(x)=mgx +m¦Ø^2x^2/2. It is shown that, while the center of the soliton obeys Newton's equation with the potential V(x), the internal structure of the soliton is determined by the Gross-Pitaeviskii equation of the "body-fixed" coordinate system. The soliton structure is found to be independent of gravity potential. Our results are verified by numerical experiments.

[D34.003] The exact N-soliton solutions of the coupled Gross-Pitaevskii equations and soliton trains in two component Bose-Einstein condensates

We investigate the behavior of diverse soliton solutions for two-component Bose-Einstein condensates with the attractive interaction by using Darboux transformation. In the context of cold atomic gases, the two vector components evolving under the Gross-Pitaevskii are the macroscopic wave functions of Bose-condensed atoms in two different internal states, which we will denote as |1> and |2>. The nonlinear interactions are due to elastic s-wave scattering among the atoms, and are effectively attractive (negative scatteriing length) for system of 7^Li in which multicomponent condensates have been realized.

[D34.004] The Small-Amplitude Solitons of Bose-Einstein Condensates in 1D Optical Lattice

Using the Bose-Hubbard model, we find that the dynamics of Bose-Einstein Condensates in 1D optical lattice can be described by the general discrete nonlinear Schrodinger equation. The dark and bright soliton solutions in small-amplitude approximation are obtained and the conditions of existence of these solitons are discussed.

[D34.005] Adiabatic theory of nonlinear evolution of quantum states

Adiabatic evolution has been an important method of preparation and control of Bose-Einstein condensates. However, it is not clear of how the adiabatic theorem gets modified considering the nonlinear interaction between the atoms. The difficulty arises not only from the lack of unitarity in the evolution of quantum states but also from the absence of the superposition princple in the nonlinear Schödinger equation. In this talk, we present a general theory for nonlinear adiabatic evolution of quantum states by utilizing the canonical structure of the Schödinger equation. Our theory not only spells out conditions for adiabatic evolution of eigenstates, but also characterizes the motion of non-eigenstates which cannot be obtained from the former in the absence of the superposition principle. Geometric phases, such as the Aharonov-Anandan phase and Hannay's angles, are found to play important roles in characterizing the response of cyclic or quasicyclic non-eigenstates to slow change of control parameters.

[D34.006] Electronic Structures and Magic Numbers of Small Silver Clusters: A Many Body Perturbation Theoretic Study * 1

The formalism of second order many body perturbation theory has been applied to investigate the electronic and geometric structures of neutral, cationic, and anionic Agn (n=5-9) clusters. Hay-Wadt relativistic effective core potentials replacing the twenty-eight core electrons and a Gaussian basis set have been used. Full geometry optimizations of topologically different clusters and clusters belonging to different symmetry groups have been carried out. The neutral silver clusters prefer planar geometry up to n=6 and the charged clusters prefer three dimensional geometry from n=6. Binding energies, ionization potentials, electron affinities, and fragmentation energies of the optimized clusters have been compared with other experimental and theoretical results available in the literature. Based on different criteria, we predict the eight-atom silver cluster to be a magic cluster.

* Work supported in part by the Welch Foundation, Houston, Texas (Grant No. Y-1525)

1 M. N. Huda and A. K. Ray, Phys. Rev. A, in press.

[D34.007] Electronic Structures of Small Gold Clusters

Ab initio second order many body perturbation theory with scalar relativistic pseudopotentials have been used to determine the electronic and geometric structures of neutral, cationic, dicationic, and anionic small gold Aun (n=2-4) clusters. We discuss, in particular, the metastability of the doubly charged clusters. For the neutral, cationic, and anionic tetramer, the rhombic structure is found to be the most stable structure. For this cluster, adiabatic ionization potential and the electron affinity are predicted to be 190.13 and 59.67 kcal/mol, respectively. Results are compared, wherever possible, with published data in the literature.

*Work supported by the Welch Foundation, Houston,Texas (Grant No. Y - 1525).

*A. K. Ray, Computational Materials Science, 25, 279-284 (2002).

[D34.008] Computational study on multiply charged metal atoms ligated with DMSO

Extensive research efforts, both experimental and computational, have focused on metal dications (M^2+)in combination with various ligand (L) systems. The recent interest in these units can be ascribed to the successful application of mass spectroscopic techniques that allow to observe metal ion - ligand complexes in the gas phase which are accessible to theoretical modeling. The stability of these systems was found to depend sensitively on both the nature and the number of ligands. Whenever the second ionization potential of M exceeds the first ionization potential of L, the system M^2+L is not thermodynamically stable but subject to electron transfer from the ligand to the metal atom followed by Coulomb explosion of the complex. However, one can identify a minimal number of ligands N_min that stabilize a complex of the form M^2+L_N. The present contribution is chiefly concerned with the interpretation of a recent series of measurements(A.A.Shvartsburg, J.Am.Chem.Soc. 124, 12343 (2002).) on various metal trications in conjunction with Dimethylsulfoxide (DMSO) ligands, demonstrating a distinct increase of N_min with the third ionization potential of the metal atom species involved. It is shown that Density Functional computations at the B3LYP level account for the experimentally established relation between these two quantities.

[D34.009] Interaction of 3d transition metal atoms with charged ion projectiles from Electron Nuclear Dynamics computation

Computational results on atomic scattering between charged projectiles and transition metal target atoms are presented. This work aims at obtaining detailed information about charge, spin and energy transfer processes that occur between the interacting particles. An in-depth understanding of these phenomena is expected to provide a theoretical basis for the interpretation of various types of ion beam experiments, ranging from gas phase chromatography to spectroscopic observations of fast ions in ferromagnetic media. This contribution focuses on the scattering of light projectiles ranging from He to O, that are prepared in various initial charge states, by 3d transition metal atoms. The presented computations are performed in the framework of Electron Nuclear Dynamics (END)^1 theory which incorporates the coupling between electronic and nuclear degrees of freedom without reliance on the computationally cumbersome and frequently intractable determination of potential energy surfaces. In the present application of END theory to ion - transition metal atom scattering, a supermolecule approach is utilized in conjunction with a spin-unrestricted single determinantal wave function describing the electronic system. Integral scattering, charge and spin exchange cross sections are discussed as functions of the elementary parameters of the problem, such as projectile and target atomic numbers as well as projectile charge and initial kinetic energy.

^1 E.Deumens, A.Diz, R.Longo, Y.Oehrn, Rev.Mod.Phys. 66, 917 (1994)

[D34.010] New Tools for Predicting the Collisional Dynamics of High Energy Molecules

Transient infrared laser probing provides exquisitely detailed information about the quantum state resolved dynamics of molecular collisions and the energy flow pathways that relax highly excited molecules and compete with reactive pathways. Recent experimental results have investigated the ways in which CO2, H2O and DCl remove energy from a series of highly vibrationally excited aromatic molecules (Evib~38000 cm-1) of increasing complexity and size: pyrazine, pyridine, 2-methyl pyridine and 2,6-dimethyl pyridine. Nascent rotational and translational energy distributions for specific vibrational states of the energy-accepting bath molecules reveal how molecular properties of the bath and donor species influence the relaxation dynamics. These data are used to generate energy transfer distribution functions of specific energy transfer pathways and the results are compared to theory using a new approach based on Fermi's golden rule.

[D34.011] Laser Induced Thermal Desorption : Application as a Probe of Metal Surfaces Covered by Gas Molecules

We have developed LITD (Laser Induced Thermal Desorption) method to study the interaction between metal surfaces and the adsorbed gas molecules. With LITD we can get good spatial resolution on metal surface which is related to our future research about quantum states resolved studies – direct measurements of the sticking coefficients. We measured TOF(Time of Flight) of the desorbed molecules using a quadrupole mass spectrometer which showed clear angle dependence of the desorption. We also measured the desorption area which is slightly different than laser beam width. Using a cylindrical lens to focus the laser beam to a strip, we measured the desorption width to be 0.17±0.02mm for a laser power of 7mJ/pulse and the angle between the beam direction and sample direction is 15^o.

[D34.012] Helium Atom Beam Induced Desorption of H2 From a Weakly Bound H2/MgO System

Usually Helium atom scattering is considered as a gentle and non-destructive technique in surface science, since it employs neutral probe particles with energies in the range of 10-80 meV. However, in the case of the weakly bound physisorbate H2/MgO with an adsorption energy of about 25 meV per molecule, the desorption of H2 molecules by the impinging He atoms is observed when the incident energy of the He beam exceeds 40 meV. Evidence of the desorption appears in two effects: (a) To maintain a particular H2 coverage on the MgO surface, the H2 gas pressure needs to be higher by more than an order of magnitude in the presence of He beam induced desorption as compared to lower beam energies where desorption does not occur. (b) Adsorption curves, i.e. the specular He signal during H2 adsorption, reveal different initial slopes, if the amount of adsorption is reduced by He beam induced desorption. The dependence of the desorption process on incident energy and He flux is discussed on the basis of simple kinetic arguments. For comparison, the similar effect of the desorption of water molecules from NaCl by an electron beam is also presented.

[D34.013] Interaction of slow (<5 keV/u), highly charged ions with nanostructured membranes

We report on studies of the interaction of slow, multiply (e. g. Ar3+) and highly charged ions (e. g. Xe44+) with silicon nitride membranes [1]. Arrays of holes are formed in thin (30 to 200 nm thick) membranes by focused ion beam drilling. Aspect ratios of holes range from 1:1 to about 5:1. Charge exchange in thin membranes is investigated as well as energy loss and foil lifetimes under ion beam exposure. We will discuss the question of capillary beam guiding [2] for high ion charge states.

[1] T. Schenkel et al., SPIE V 4656, 10 (2002), J. Vac. Sci. Technol. B in press (2002) [2] N. Stolterfoht, et al., Phys. Rev. Lett. 88, 133201 (2002)

[D34.014] Effective unified model for nuclear strong and weak interactions

About 500 papers were presented at the APS Nuclear Physics conference at Michigan State Univ. in Oct. of 2002. The most recent high-energy research was discussed, much of which centered on the results of p + p, Au + Au, and included ion to fixed-target collisions. Papers included related research on nuclear mass defect demonstrated by common electron capture events, 7Be + -e -> 7Li + v, neutron decay, n -> p + -e + -v and other nuclear events. Of particular importance is the fact that every nucleus contains nucleons that differ in mass from element to element. Nuclear magnetic moment (b-NMR), quadrupole moment and charge transformation were discussed. One scientist stated that, to remain useful, the Standard Model (SM) scheme requires no less than 89 fundamental particles. When experiment and prediction do not agree, such models are subjected to continuous modification. It was not surprising that a large number of speakers concluded with a call for a new nuclear model. As an alternative to a fractionally charged system, we propose an elegant Geatron Model consisting of whole fundamental charges. It is an effective model and unified theory for the nuclear strong and weak interactions and other nuclear occurrences. This system comprises just 3 distinct fundamental particles rather than the 89 relied upon by current models. It predicts the existence of 38 rudimentary particles that are the first possible arrangements of the 3 fundamental units. The model makes numerous verifiable predictions, identifies the exact point of origin of the known forces and describes the processes related to the formation of matter. Potential scientific, industrial and commercial applications that emerge from this flexible model may be substantial.

[D34.015] Mesoscopic effects and radiative coupling between lasing modes in a random laser

Random lasers are systems, in which lasing occurs due to effects of multiple scattering of light in a random media rather than due to a light confinement in a cavity. Current theoretical research in this area is mostly focused upon studying statistical properties of lasing threshold assuming that the electromagnetic field remains uniform within the excited volume [1]. Other approaches rely on numerical simulation of one-dimensional systems [2], in which, of course, all effects due to inhomogeneous electromagnetic field distribution in space are taken into account. This approach, however, does not give a clear qualitative understanding of properties of random lasers. In the present work we study qualitative effects of the spatial mesoscopic fluctuations of the field on the mode structure and the lasing threshold of a random laser. We present a simple analytical model showing that the mesoscopic structure of the field can result in radiative coupling between two lasing modes and lead to their synchronization, which was observed recently in Ref. [3]

The author would like to thank Hui Cao for providing the results of Ref.[3] prior to publication.

References

[1] A. L. Burin, Mark A. Ratner, H. Cao, and S. H. Chang. Phys. Rev. Lett. 88, 093904 (2002)

[2] Xunya Jiang and C. M. Soukoulis, Phys. Rev. Lett. 85, 70 (2000)

[3] H. Cao, Xunya Jiang, Y. Ling, J.Y. Xu, C.M. Soukoulis. Submitted to PRL.

Part D of program listing

Please note that the information contained in this writing along with every subject presented here will be included with full details in the author's new book on the general subject of Fundamental Particle Physics that will be published in the Fall of 2005.

Eugene B. Pamfiloff
boris@2xtreme.net
 

Copyright  © 1999 - 2005 by Eugene B. Pamfiloff